Arithmetic Sequence and Series?

Question

3, 7, 11, 15...

The question: The first 4 terms in a sequence are shown above. Each term after the first is found by adding "x" and to the term immediately preceding it. Which term in the sequence shown above is equal to 147?

The answer: 37

The formula: 3+4 (n-1)= 147

In the formula, I don't understand where and what "n" is and equals.

and please state why you subtract "1".

Answer 1

3, 7, 11, 15...
The formula: 3 + 4(n-1)= 147
The series is developed by adding 4 to the previous number.
The first number is a 3
You want to add 4 to 3 how many times to get 147
But since we want to know the total number and we all ready have used one (the 3), we take the 3 away from n.
That is where the term (n-1) comes from
Solving 3 + 4(n-1)= 147
4n-4 = 144
n= 37 meaning that there are a total of 37 numbers before the final number of 147 is reached in this series

Answer 2

n corresponds to the term you are referring to. For example, if n=1, then you are talking about the first term, n=2 about the 2nd etc. So in this particular example

3 + 4(n-1)=147 => n=39.

So the 39th term of the sequence is equal to 147.

Answer 3

n is the number of the term
in the example the value of the 37th term is

3+4(37-1)=147
3+4(36)=147
3+144=147
147=147